Mathematische Zeitschrift

, Volume 268, Issue 1, pp 45–66

On the Cauchy problem for the two-component Camassa–Holm system


DOI: 10.1007/s00209-009-0660-2

Cite this article as:
Gui, G. & Liu, Y. Math. Z. (2011) 268: 45. doi:10.1007/s00209-009-0660-2


In this paper we establish the local well-posedness for the two-component Camassa–Holm system in a range of the Besov spaces. We also derive a wave-breaking mechanism for strong solutions. In addition, we determine the exact blow-up rate of such solutions to the system.


Besov spaces Blow-up Local well-posedness Two-component Camassa–Holm system Wave-breaking 

Mathematics Subject Classification (2000)

35G25 35L15 35Q58 

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsJiangsu UniversityZhenjiangChina
  2. 2.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  3. 3.Department of MathematicsUniversity of TexasArlingtonUSA

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